In Batman: Arkham City, there is an achievement/trophy called Perfect Freeflow 2.0, described as Perform a perfect combo including all of Batman's combat moves (any play mode).

What are all the moves that have to be done, and is there a recommended place and order to do them in to get this achievement? Apart from finding a good place to do this, I feel like I must be missing a few moves as I was pretty sure I'd get this a few times.

You can supposedly use any 1 gadget, but the Combo Batarang is the simplest to fire off quickly and reports vary on which ones count, so this is the safest

Finishers

Ground Pound 360: (RT+ⓨ) PS3: (R2+△)

For finishing off dazed enemies on the ground

Special Combo Takedown 360: (Ⓑ+ⓨ) PS3: (△+◯)

Beat Down Finisher 360: (Ⓑ, ✕repeatedly) PS3: (◯,□ repeatedly)

Good places to complete this are the Survival of the Fittest Challenge Map or on the Joker's Carnival DLC Map (if you have that available to you). You should definitely get as many combat upgrades as possible, or at the very least, get the Special Combo Boost and Freeflow Focus upgrades. Critical Strikes will also help build your multiplier faster.

It took me about two hours to earn this trophy/achievement. I spent the first 90 minutes developing a strategy. I then had to memorize it.

I used the Survival of the Fittest challenge map. There aren't any Titan henchman, lieutenants, armored thugs, or shielded thugs in this challenge map. Those guys are really good at landing a hit and breaking the combo. Unfortuantely, there won't be enough enemies until the third and fourth rounds (I earned my trophy the third round). If you're really precise on your combo timings, you might be able to get it in the second round.

Here's my strategy:

As soon as the action starts, do a Batclaw Slam (360: tap LT+✕,Ⓧ; PS3: tap L1+△,□). This will launch you into the crowd of thugs, so be prepared to immediately Counter (360: ⓨ; PS3: △), Strike (360: Ⓧ; PS3: □), and Evade (360: Ⓐ,Ⓐ; PS3: ✕, ✕). Sometimes a thug will run up to you fast and you'll have to Counter before completing the slam. If this happens, continue re-trying the slam.

Once your in the crowd of thugs, build up your combo until you reach a critical strike, then do a Special Combo Multi Ground Takedown (360: Ⓐ+Ⓑ; PS3: ✕+◯). Do this combo first because it's early enough in the fight that anybody on the ground is usually dazed. If you wait until later, you increase the chances that enemies on the ground are defeated not dazed and you'll break your flow. Plus, you immediately get to take out two to four attackers, which helps later.

Strike, Counter, and Evade to get to the next critical strike and do a Special Combo Disarm and Destroy (360: ✕+ⓨ; PS3: (△+□). You don't have to be aiming at any armed enemies. The game will find one for you and send Batman screaming across the room at him, if necessary.

Build up your combo again, and at the next critical strike, do a Special Combo Takedown (360: Ⓑ+ⓨ; PS3: △+◯), preferably in the direction of an enemy with a blade.

Continue to Strike, Counter, and Evade until the next critical strike. Do a Special Combo Bat Swarm (360: Ⓐ+✕; PS3: □+✕). As Batman is up in the air, use the camera to look around and find the most isolated enemy. When the combo finishes, aim toward your chosen victim, and do a Beat Down Finisher (360: Ⓑ, ✕repeatedly; PS3: ◯,□ repeatedly). If someone attacks during the beat down, counter, then continue.

Batman will usually have most enemies behind him, out of camera shot, toward the end of the beat down. During the move's finish, Batman will have a couple seconds of invincibility. Swing the camera around so you can see the enemies again.

At this point, you should have a critical strike ready. Stun (360: Ⓑ; PS3: ◯) the nearest enemy, then launch the Bat Swarm combo again. This gives you a little bit of breathing room.

For your last two movies, you want to finch the most isolated enemy in the room. If you're lucky, there's someone all the way across the room, cowering in a corner or holding up a fire extinguisher like a trophy. If not, Strike, Counter, and Evade until you've built up another critical strike and do a Bat Swarm combo to daze the enemies and pick a good target.

Once you've picked the most isolated enemy, do the Ultra Stun (360: Ⓑ,Ⓑ,Ⓑ; PS3: (◯,◯,◯). This move knocks an enemy to the ground, so follow it immediately with a Ground Pound (360: RT+ⓨ; PS3: R2+△). Both the ultra stun and ground pound take a couple seconds and leave Batman completely vulnerable and unable to Counter so make sure you're attacking a very isolated enemy. You could also wait for the last man standing.

That's it! Here are some other techniques that helped:

If you get interrupted in the middle of your flow, don't start over! You'll never memorize the second half of the sequence if you start over. The second half requires precise timing. You must practice it. If your flow is interrupted, continue with the next move in the sequence. Try to get to the point where you know the sequence well enough that you don't really think about what comes next. Your brain and hands just know and you can think about camera angles, scanning the room, looking for counter icons, etc.

As soon as you hit the keys to do a special combo, you're momentarily invincible. This is a good time to look around the room and find the direction of you next attack.

Some enemies will hold a fire extinguisher or other combustible container, waiting for an opportunity to throw it at you. If you can destroy it with a Batarang or a Disarm and Destroy combo, the explosion will disorient most of the enemies and give you some space to focus.

Evade any enemies that attack with a blade (the yellow counter icon). I never mastered the Blade Dodge.